WASHINGTON — As the White House made a final push for ObamaCare sign-ups before Monday’s deadline, a Republican lawmaker accused the administration of “cooking the books.”

“I don’t think it means anything,” Sen. John Barrasso (R-Wyo.) said of the Obama administration boasting that a flood of last-minute sign-ups had boosted enrollment within striking distance of its goal of 7 million.

President Obama announced last week that enrollment had topped the 6 million mark, although the government figure does not represent how many people paid for and actually obtained insurance coverage.

“People want to know the answers to that,” Barrasso said on “Fox News Sunday,” adding that questions also remain about what kind of insurance people get, how much it costs and whether they can keep their doctors.

The administration has racked up higher enrollment numbers than few possible during the glitch-plagued rollout of the ObamaCare Web site, HealthCare.gov, in October.

But the White House also announced another delay for the law, granting Americans who have begun the enrollment process a two-week grace period to finish signing up after the March 31 deadline.

Still, the health-care measure remains unpopular with most voters, and the issue threatens to flip control of the Senate to the Republicans in this year’s elections.

Sen. Angus King, a Maine independent who caucuses with Democrats and who led a group of vulnerable Obama allies in proposing fixes to the law, predicted the administration would reach its goal of 7 million sign-ups. He said more than 6.5 million had enrolled as of Sunday morning.

“I checked the numbers this morning,” King said on the same show with Barrasso. “And those numbers don’t come from the White House.”

King’s legislation would exempt more businesses from the employer mandate and give Americans the option of lower-cost, higher-deductible plans, which are some of the same types of plans that many have lost.

“It’s time to try to fix it,” said King. “That’s what the public wants.”

But Senate Majority Leader Harry Reid (D-Nev.) said the bill won’t get a vote, likely avoiding a battle over GOP amendments to further alter or repeal ObamaCare.

“[King’s] legislation only nibbles around the edges,” said Barrasso. “It doesn’t get to the fundamental flaws of the president’s health-care law.”